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DTSTART;TZID=America/Toronto:20240125T153000
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URL:https://uwaterloo.ca/pure-mathematics/events/special-colloquium-57
SUMMARY:Special Colloquium
CLASS:PUBLIC
DESCRIPTION:LENA JI\, UNIVERSITY OF MICHIGAN\n\n\"RATIONALITY OF ALGEBRAIC 
 VARIETIES OVER NON-ALGEBRAICALLY-CLOSED\nFIELDS\"\n\nThe most basic algebr
 aic varieties are projective spaces\, and their\nclosest relatives are rat
 ional varieties. These are varieties that\nagree with affine space on a de
 nse open subset\, and hence have a\ncoordinate system on this open subset.
  Thus\, rational varieties are\nthe easiest varieties to understand. Histo
 rically\, rationality\nproblems have been of great importance in algebraic
  geometry: for\nexample\, Severi was interested in finding rational parame
 trizations\nfor moduli spaces of Riemann surfaces (algebraic curves). Over
  the\ncomplex numbers\, techniques from geometry and topology can be used 
 to\nextract invariants useful for rationality questions. Over fields that\
 nare not algebraically closed (such as the rational numbers)\, the\narithm
 etic of the field adds additional subtleties to the rationality\nproblem. 
 When the dimension of the variety is at most 2\, there are\neffective crit
 eria to determine rationality. However\, in higher\ndimensions\, there are
  no such known criteria. In this talk\, I will\nfirst give a survey of som
 e results on rationality of algebraic\nvarieties. Then I will explain resu
 lts on rationality obstructions for\nhigher-dimensional varieties that inv
 olve the arithmetic of the field.\n\nM3 3127
DTSTAMP:20260505T152524Z
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